The maximum area of a rectangle whose two vertices lie on t…

Maths Definite Integral and Area Under Curves General Single Correct MCQ

Published on: August 14, 2026

The maximum area of a rectangle whose two vertices lie on the x-axis and two on the curve y = 3 – |x|, – 3 ≤ ≤ x ≤ ≤ 3 is

9/2

None of these

Text Solution

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The correct answer is:

The area bounded by the lines

y = 3 -|x|, – 3 ≤ ≤ x ≤ ≤ 3 is shown in the fig.

Area A(x) = 2x .(3-x)

⇒ ⇒ A ′ ′ (x) = 2 (3-x) –2x

= 6 – 4x = 0 ⇒ ⇒ x = 3/2

⇒ ⇒ Maximum area of the rectangle occurs when x = 3/2.

Maximum area=2. sq. units

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